I thought that the reason for banning Kaspersky was simply that they had annoyed the NSA by finding the Fed's super-duper spying software. This was even before the whole Snowden business and the tools leak. We all knew that the NSA was up to something but it took Snowden to reveal the extent of the hacks.
Unlike many I'd guess that Kaspersky is more of a nuisance than an asset to the Russians. It must have occurred to the Russians years ago that their systems were likely to be hacked -- after all, they had plenty of home grown hackers going at everyone's systems. They might be on the inside track for Trojan discovery but if they're anything like other intelligence services from time immemorial they'd keep very quiet about it because if there's one thing better than knowing what your adversary's up to its them not knowing you know. They'd want a Kaspersky not to go digging among the pro stuff but just to occupy itself with the latest credential stealing phishing attack -- they'd need to be good, but not too good (just like the run of the mill AV companies, come to think of it).